对象化理论及其应用的初步研究

【作者】 王茜；

【导师】 冯振举；

【作者基本信息】 曲阜师范大学 ， 教育硕士（专业学位）， 2024， 硕士

【摘要】 数学概念是数学学科的起点,是数学思维的核心。在中学数学教学中,数学概念教学占据着基础且关键的地位,是培养学生数学抽象等数学学科核心素养的重要途径,对学生后续学习其他数学知识产生深远影响。但是,在实际教学中,数学概念课尚存在着“重记忆、轻理解”“重结果、轻过程”等问题,易造成“学生对数学概念的认知尚未达到应有的抽象水平”“学生难以清晰表达其对数学概念的理解认识”等异化现象。这种教学严重影响着学生数学思维、数学能力的发展,不利于我国数学教育目标的落实。为此,本文介绍并梳理了由拉德弗德教授提出的对象化理论,在其指导下以《函数的单调性》一课为例,探索改进高中数学概念教学的路径和方法。本文采用文献研究、访谈、质性分析、课例研究等方法,阐明引入对象化理论的必要性,构建基于对象化理论的活动分析框架,分析并解释高中数学概念教学活动,以此了解当前教学活动是否满足对象化理论对课堂活动的要求。同时,在课堂观察分析的基础上,以对象化理论为指导重新设计、实施并改进《函数的单调性》教学,考察对象化理论对于高中数学概念教学的有效性。通过上述研究过程,本文得出如下主要研究结论。首先,对象化理论紧扣数学学科特点,是一类立意新颖、观点较为全面、发展较为成熟的数学教育理论;其次,该理论旨在通过“联合劳动”解决课堂中的异化现象,且基本理念与我国数学教育要求相一致,将其应用于数学概念教学研究是必要的;最后,结合质性分析结果,对象化理论对于高中数学概念教学具有积极作用。本文还从教学理念、教学原则、教学策略等方面为高中数学概念教学提供可借鉴和参考的教学建议:(1)与时俱进,加强理论学习、及时更新教学理念;(2)循循善诱,关注学生由感性认识向理性认识的跨越;(3)精进策略,先教会学生表达再放手让学生表达;(4)因地制宜,探索适合我国数学概念教学的对象化理论实施路径。更多还原

【Abstract】 Mathematical concepts are the starting point of mathematics and the core of mathematical thinking.Mathematical concept teaching occupies a fundamental and key position in secondary mathematics education,and students’ knowledge and understanding of concepts have a farreaching impact on their subsequent learning of other mathematical knowledge.However,in actual teaching,mathematical concept classes still exist problems such as "emphasizing memorization,light on understanding","emphasizing the result,light on the process",etc.It is easy to lead to the emergence of alienation phenomena such as "students’ knowledge of mathematical concepts has not yet reached the proper level of abstraction" and "it is difficult for students to clearly express their understanding of mathematical concepts".This kind of teaching seriously affects the development of students’ mathematical thinking and mathematical ability,and is not conducive to the implementation of the goals of mathematics education in China.Therefore,this thesis introduces and combs the Theory of Objectification proposed by Professor Radford,and under its guidance takes the lesson of "Monotonicity of Functions" as an example to explore the paths and methods to improve the teaching of high school mathematics concepts.This thesis adopts the methods of literature research,interview,qualitative analysis,and classroom case study to clarify the necessity of introducing the Theory of Objectification,construct an activity analysis framework based on the Theory of Objectification,and analyze and explain high school mathematics concept teaching activities,so as to find out whether the current teaching activities meet the requirements of the Theory of Objectification for classroom activities.Based on classroom observation and analysis,this thesis redesigns,implements,and improves the teaching of "Monotonicity of Functions" under the guidance of the Theory of Objectification to test the effectiveness of the Theory of Objectification in high school mathematics concept teaching.Through the above research process,this thesis draws the following main conclusions.Firstly,the Theory of Objectification captures the characteristics of the mathematics discipline,and it is a kind of mathematics education theory with a novel intention,a more comprehensive viewpoint and a more mature development.Secondly,the theory aims to solve the alienation phenomenon in the classroom through "joint labor",and its basic concept is consistent with the requirements of mathematics education in China,so it is necessary to apply it to the study of mathematics concept teaching.Finally,combined with the results of qualitative analysis,the Theory of Objectification has a positive effect on high school mathematics concept teaching.In addition,the thesis provides pedagogical approaches that can serve as references for senior high school mathematics concept teaching from the aspects of teaching philosophy,teaching principles,teaching strategies.(1)Stay current with the latest developments in theory and update educational ideas in time;(2)Guide patiently and systematically,focuses on the students’ leap from perceptual to rational understanding;(3)Refine the strategy,teach students to express,then let them express;(4)Explore the implementation path of the Theory of Objectification that is suitable for teaching mathematical concepts in accordance with local conditions.更多还原